In this paper, we introduce the notion of Euclidean module and weakly Euclidean ring. We prove the main result that a commutative ring R is weakly Euclidean if and only if every cyclic R-module is Euclidean, and also if and only if End( R M ) is weakly Euclidean for each cyclic R-module M . In addition, some properties of torsion-free Euclidean modules are presented.